Medical physics (A-level only)

Explanation

• The eye is an optical refracting system. The cornea provides most refraction, while the lens changes power during accommodation so that a real, inverted image forms on the retina.
• Ray diagrams should show refraction at the eye and convergence onto the retinal surface.
• Cones work best in bright light, give colour vision and provide high spatial resolution because there is little convergence of their nerve pathways.
• Rods are more sensitive at low light levels and many feed one nerve pathway, increasing sensitivity but reducing spatial resolution; rods do not distinguish colour.
• The eye's sensitivity also depends on wavelength, so its spectral response changes with the active receptor cells and lighting conditions.

Explanation

• Lens power is $P=1/f$, with $f$ in metres and power in dioptres; a converging lens has positive power and a diverging lens negative power. Using the real-is-positive convention, $1/f=1/u+1/v$ and $m=v/u$, so a virtual image distance is negative.
• Myopia makes distant objects focus in front of the retina and is corrected by a diverging lens.
• Hypermetropia prevents nearby objects focusing on the retina and is corrected by a converging lens.
• Astigmatism gives different focusing in different planes and is corrected using a cylindrical component; a prescription states its cylindrical power and an axis from $0^\circ$ to $180^\circ$.
• Ray diagrams must show how the correcting lens changes convergence.

Explanation

• The pinna and ear canal direct pressure variations in air to the tympanic membrane, which vibrates at the sound frequency.
• The ossicles transmit this mechanical vibration through the middle ear and act as a lever system.
• Because the oval window has a smaller area than the tympanic membrane, the transmitted force produces a larger pressure in the inner-ear fluid.
• Pressure waves in the inner-ear fluid stimulate receptors, which produce electrical impulses in the auditory nerve.
• A complete explanation follows the energy transfer in order: air pressure variation, membrane vibration, ossicle motion, fluid pressure wave, receptor stimulation and electrical nerve signal.

Explanation

• Sound intensity is power transferred per unit area, measured in $\text{W m}^{-2}$; an isotropic point source gives $I=P/(4\pi r^2)$. Intensity level is $L=10\log_{10}(I/I_0)$ in decibels, where $I_0=1.0\times10^{-12}\,\text{W m}^{-2}$.
• The logarithmic scale reflects perception and compresses a very wide intensity range.
• Equal-loudness curves show the level required at each frequency for the same perceived loudness; lower curves mean greater sensitivity, normally around a few kilohertz.
• A relative level is $\Delta L=10\log_{10}(I_2/I_1)$.
• The dBA scale applies frequency weighting to approximate human response, whereas an unweighted dB value represents the physical intensity ratio alone.

Explanation

• Hearing loss means that a greater sound intensity level is needed to produce the same perceived loudness.
• On an equal-loudness or threshold graph, the affected curve shifts upward over the frequencies where sensitivity has fallen.
• The hearing loss at a stated frequency is the vertical difference in decibels between normal and impaired curves, not the horizontal frequency separation.
• Deterioration with age commonly produces greater loss at high frequencies, while injury from prolonged excessive noise may produce a pronounced loss over a narrower frequency range, often near $4\,\text{kHz}$.
• The required account concerns the change in sensitivity and its representation on equal-loudness curves; unsupported detail about physiological damage is outside this specification point.

Explanation

• Skin electrodes measure small potential differences produced by electrical activity in the heart. Conductive gel, prepared skin and secure contacts reduce resistance and movement artefacts; a high-gain, low-noise differential amplifier and shielded leads are needed because signals are of order millivolts.
• On a normal waveform, the P wave represents atrial depolarisation, the QRS complex ventricular depolarisation and the T wave ventricular repolarisation.
• Heart period is measured between equivalent points, usually successive R peaks, and $\text{rate}=60/T$ when $T$ is in seconds.
• Measuring across several cycles reduces percentage uncertainty.
• An ECG records electrical potential difference, not blood pressure, blood flow or the heart's mechanical force.

Explanation

• Acoustic impedance is $Z=\rho c$. At a boundary, the reflected intensity fraction is $I_r/I_i=((Z_2-Z_1)/(Z_2+Z_1))^2$; a larger mismatch gives a stronger echo and less transmission.
• Coupling gel removes air between transducer and skin, reducing mismatch. A piezoelectric crystal converts a short alternating potential difference into an ultrasound pulse and converts returning deformation into a detected potential difference.
• Echo depth is $d=ct/2$ because the pulse travels out and back. A new pulse is sent only after the deepest echo returns, so the maximum pulse-repetition frequency is set by the two-way travel time.
• Higher frequency improves resolution but increases attenuation. An A-scan displays echo amplitude against time or depth; a B-scan maps echo brightness and position into a two-dimensional image.
• Ultrasound is non-ionising and real-time, but air and bone boundaries limit access and resolution.

Explanation

• An optical fibre has a higher-refractive-index core surrounded by lower-index cladding. A ray travelling in the core undergoes total internal reflection when it meets the boundary from higher to lower index at an angle greater than the critical angle.
• Cladding also keeps light within each fibre and reduces cross-talk.
• In a flexible endoscope, a non-coherent bundle carries illumination because fibre order need not be preserved.
• A coherent bundle keeps fibres in the same relative positions at both ends, so each fibre transfers one part of the image.
• Flexible bundles allow internal imaging through a small opening and can also guide treatment light, reducing the need for more invasive access.

Explanation

• An MR scanner uses the strong field of a superconducting magnet to align hydrogen nuclei, or protons, with spins parallel; the spinning nuclei precess about the magnetic field lines. Gradient coils vary the field with position so successive small regions of a patient cross-section can be selected and located.
• A short radio-frequency pulse excites protons in a selected region and changes their spin state. As the protons de-excite after the pulse, they emit radio-frequency signals.
• The emitted radio-frequency signal has the same frequency as the exciting pulse. Receiver coils detect these signals and a computer processes their position and strength to construct a visual cross-sectional image.
• MR uses non-ionising radio waves and magnetic fields.
• Production of the fields and detailed relaxation times are not required.

Explanation

• Thermionic emission releases electrons that accelerate through potential difference $V$ and decelerate at a metal target. Most energy becomes heat, so a rotating anode spreads heating.
• Different electron energy losses produce the continuous X-ray spectrum; $E_{\max}=eV$ and $\lambda_{\min}=hc/(eV)$. Characteristic lines occur when incident electrons remove inner-shell electrons and higher-shell electrons fall into vacancies.
• Increasing tube current increases intensity and patient dose, while increasing voltage raises maximum photon energy and penetration.
• A smaller focal spot improves sharpness but concentrates heating.
• Filtration removes low-energy photons and collimation restricts the exposed region, controlling dose and image quality.

Explanation

• In a flat-panel detector, a scintillator converts X-rays to visible photons, photodiode pixels convert light to electrical charge, and electronic scanning transfers pixel signals to a computer. The immediate digital image can be enhanced, stored and transmitted; high sensitivity and wide dynamic range may reduce repeat exposures compared with film.
• X-rays darken photographic film, while an intensifying screen converts X-rays to visible light so less dose is needed.
• Fluoroscopic image intensification gives live images, although prolonged viewing can raise dose.
• X-ray-opaque barium absorbs strongly and outlines low-contrast digestive structures against soft tissue.
• Images arise from differential transmission and absorption, not reflected X-rays.

Explanation

• For a narrow monoenergetic beam, transmitted intensity follows $I=I_0e^{-\mu x}$, where $\mu$ is the linear attenuation coefficient and $x$ is thickness in compatible units. Attenuation is exponential, not a fixed subtraction per unit thickness.
• The half-value thickness is $x_{1/2}=\ln2/\mu$; after $n$ half-value thicknesses, $I=I_0(1/2)^n$.
• The mass attenuation coefficient is $\mu_m=\mu/\rho$, with SI unit $\text{m}^2\,\text{kg}^{-1}$, allowing materials to be compared without density's direct effect.
• Bone and contrast media attenuate more strongly than soft tissue, so differential transmission creates image contrast.
• The equation gives transmitted, not absorbed, intensity.

Explanation

• A CT scanner moves an X-ray tube around the patient and directs a narrow, approximately monochromatic beam through the body to an array of detectors. At many angles, detectors measure the transmitted intensity along different paths.
• A computer combines these projections to reconstruct a cross-sectional visual image; successive slices may form a three-dimensional representation.
• CT removes the superposition of structures in a plain radiograph and provides better localisation and useful soft-tissue information.
• Its disadvantages are greater cost and usually a higher ionising-radiation dose than a simple X-ray image.
• Required comparisons are limited to image resolution, cost and safety; detector construction and operation are not required.

Explanation

• A tracer combines a gamma-emitting radioisotope with a compound that has affinity for a chosen organ; penetrating gamma photons leave the body for external detection. Technetium-99m emits about $140\,\text{keV}$ gamma radiation, has a roughly $6\,\text{h}$ half-life and labels many compounds.
• Iodine-131 is taken up by the thyroid, emits beta and gamma radiation and has a roughly $8\,\text{d}$ half-life. Indium-111 emits gamma radiation and has a roughly $2.8\,\text{d}$ half-life.
• Higher gamma energy makes collimation harder because photons can penetrate the lead between adjacent collimator holes, and it lowers detection efficiency because fewer photons are fully absorbed by the detector crystal.
• A molybdenum-technetium generator supplies fresh technetium-99m from longer-lived molybdenum-99.
• PET detects two nearly opposite $511\,\text{keV}$ annihilation photons in coincidence to locate positron-emitting tracer activity.

Explanation

• Physical half-life $T_P$ is the time for half the unstable nuclei to decay and is a property of the radionuclide. Biological half-life $T_B$ is the time for biological processes to remove half the tracer from an organ or body, ignoring radioactive decay.
• Effective half-life $T_E$ describes the combined reduction caused by both processes.
• The rates add, so $1/T_E=1/T_B+1/T_P$; consequently $T_E$ must be shorter than both component half-lives.
• All values must use the same time unit before reciprocals are combined.
• The equation concerns the amount or activity remaining in the body, not a change in the radionuclide's intrinsic physical half-life.

Explanation

• A gamma camera's lead collimator absorbs photons travelling in unsuitable directions, so accepted photons retain directional information; narrower holes improve spatial resolution but reduce count rate. A scintillation crystal converts each absorbed gamma photon into a visible-light flash and a light guide distributes it to photomultiplier tubes.
• At each photocathode, light ejects photoelectrons.
• Successive dynodes held at increasing potentials produce secondary emission, multiplying the electron number into a large anode pulse.
• Relative photomultiplier outputs locate the flash, while pulse size estimates photon energy so scattered photons can be rejected.
• A computer accumulates many accepted event positions to form the tracer-distribution image.

Explanation

• External radiotherapy directs high-energy X-rays into a tumour.
• Their penetration delivers energy at depth, where ionisation damages DNA and prevents successful cell division.
• Several beam directions can converge on the tumour: the target receives the combined dose, while each region of healthy tissue lies in fewer paths and receives less dose.
• Collimation shapes each field, shielding protects selected regions, and imaging plus computer planning locate the tumour and choose beam directions.
• Healthy tissue cannot receive zero dose, so treatment planning balances tumour control against damage to surrounding organs.

Explanation

• Brachytherapy places sealed radioactive sources inside or very close to a tumour, producing a high local dose while reducing irradiation of distant tissue. Beta-emitting implants are suitable because beta particles are ionising but have a short range in tissue; a more penetrating gamma source would expose more healthy tissue beyond the target.
• Several small sources can distribute dose through an irregular tumour. Activity, half-life, source position and treatment time determine the delivered dose, and temporary implants can be removed after the planned exposure.
• Staff exposure is limited by short handling times, distance, shielding and remote handling tools.
• The benefit must be linked to localisation of dose, not merely to beta being less penetrating.
• When the activity falls appreciably during a treatment, the number of decays is $N_0(1-e^{-\lambda t})$ with $N_0=A_0/\lambda$, not $A_0t$.

Explanation

• Plain X-rays are fast, available and resolve bone well, but use ionising radiation, superpose structures and give poor soft-tissue contrast. CT improves localisation through cross-sectional images but generally costs more and gives a higher ionising dose.
• Ultrasound is portable, inexpensive, real-time and non-ionising, but is operator-dependent and transmits poorly through bone or gas.
• MR gives excellent soft-tissue contrast without ionising radiation but is slower, costly and less convenient for some patients.
• Radionuclide and PET scans reveal physiological function, yet require internal ionising tracers and usually have lower spatial resolution.
• A valid comparison applies resolution, safety and convenience to the specified organ and diagnostic purpose.